During the explosion, each fission event causes >1 additional fission events. Let's say it causes 1.1 more.

As a rough rule of thumb, if something is increasing by X% per step, it doubles in 70/X steps. So in this case, at a 10% increase per step, it doubles every 7. And since each step here takes a tiny, tiny fraction of a second, this doubling can happen many, many times within a slightly less tiny fraction of a second. A rough estimate for the step time here is about 10 nanoseconds (that's 1/100 million of a second), so you're doubling in less than 100 ns, you've doubled more than ten times within 1000 ns = 1 microsecond, and you've doubled more than a hundred times within 10000 ns = 10 microsecond. (It turns out that you don't actually get this far, for reasons we'll see in a second.)

If you naively continue this process) you've doubled more than a thousand times within 100 microsecond (= 0.1 millisecond). 1000 doublings is 2^1000 = 10^300 or so. Since there aren't even 10^300 atoms in the entire Universe, this obviously can't be the case. In fact, even 2^100 = 10^30 or so is beyond the number of atoms in a supercritical chunk of normal nuclear materials.

But nothing about our math is wrong here. Instead, something must be wrong with our assumption that this process continues the way we've modeled it here. And the reason it doesn't - and hence the answer to your question - is that the developing nuclear blast starts to split its fuel apart. To make it explode in the first place, you needed to compress the fuel into a small area, so that the neutrons emitted by each fission event can be captured by other atoms of your fuel. Once the fuel isn't compressed into a small area, the number of fission events caused by each fission event (our 1.1 above) goes down, and we can no longer model the explosion's progress as a raw exponential curve. Once it falls below 1, the reaction starts to slow, and if it's much below 1, it slows down quickly.

In practice, once it is below 1 in a nuclear explosion, you've already got a very violent explosion blasting the fuel apart. So it very quickly drops far below 1, and any energy release past that point isn't caused by the initial chain reaction. This isn't quite the end of the the energy release, since the decay products from the initial chain reaction are also exceptionally radioactive and themselves quickly decay, but even those quick decays are minor-ish contributors to a nuclear explosion because their time frames are much longer than the duration of a nuclear blast (usually, anyway).